Th€ Cognitive Pßychology of Knowl€dge
G. sE{be
üd K.F. Wmdd (Edilors) Scierce Publishd! B.V. All
@ 1993 Elsevier
rights rsened.
CHAPTER
11
THE ACQUISITION OF FUNCTIONAL PLANNING AND PROGRAMMING KNOWLEDGE: DIAGNOSIS,
MODELING,AND USER.ADAPTED HELP' Claus Möbüs and Olaf Scfuödet
Univeßity of Oldelburg, Germany
ABSTRAC'] A thEelev€l
app.oach 10 model processes of prcblem solving and fic acquisidon and optimization of knowledSe was developed. Fiß1. a gene.al theorctical fmewo.k des.ribes problem solving phasss, impN driven knowl€dge acquisirion, and sucess driven knowledg€ optimiätion. Second, a Slale Model ofhyporherical intemediale knowledte stales may b€ used for or iDe diaSnos€s ol leamer's domain knowledge Änd for gen€mring tearncFadapted help md infomation. Third, a Process Model closes rhe gap belween the rheorelical frarnework and the Slare Model. The approach enables a variety ofempi.ical predictions abour pmbl€m solvint aclions, acdon and tme constlainß, and effecrs of help informarion. In addition, it har implicalions fo. rhe design of intelligenl knowledge comnnnicadon sysßns. The ABSYNT Pmblem Solving Mo.ilor (PSM) eas developed iD line with these design eqüi.emenß. It supporrs lem€l! acquisilion of basic p.ogmmminS conceprs while wo*ing in ä visual, funcdoml progImminS language. The lemer may tesr hyporhess about solutioü proposals, plans üd inlendons. and incomplete plan fagmenrs. Thrs help is supplied al impass, üe us€ of peknowledge i! €ncoDraged, and diffeßnt probtem solvine pha$s aß suppoded. In addirion, a Slate Model is designed 10 supply help adapted l() rhe curßdr knowledge shte of üe leafrer.
The development olexecutable ftodels ofhuman information processing and their empirical validation has become an important research area, especially
I
Tho rcsearch €poned hercin was financially supponed by cnnr No. Mo 29213-3 of the Deut-sche ForshunSsgemeinschaft 10 Claus M öbus and Huns Colonius.
231
234
C. Mitbus and O.
S.hrnA.,
conceming processes of knowledge acquisition. Since models of this kind explicidy represent hypothetical knowledge structures and processes, they enable detailed hypotheses conceming tbe representation and change ol knowledge, and they enable detailed and sometimes surprising predictions. Thus, they contribute to psychological theorizing and to basic research. On the
other hand, modeling the acquisition and change of knowledge is also one necessary condition for the design of individualized instruction and help for computer based systems. Individualized, user-centered, online instruction and help not only enhances kllowledge acquisition processes, but is also important for the design and development of various software tools. For example, the acceptance of such tools may depend on their sensitivity to the actual knowledge and intertions of the user.
The topic of our project has been to empirically investigate and to model processes of the acquisition, utilization, and optimization ofknowledge while working with the, BSUNZ Problem Solvitg Monitor (PSM). The ABSYNT PSM is design€d to suppofi the acquisition ofbasic functional programming concepts by supplying leamers with individualized, adaptive online helpand proposals. ABSYNT ("Abstract Syntax Trees") is a functional visual prcgramming language developed in the project. The ABSYNT PSM provides help for the leamer constructing ABSYNT programs to accomplish given tasks.
The design and development of a system like the ABSYNT PSM is not possible without creating models representing knowledge states and knowledge acquisition processes of leamers. Our system is embedded in a three kvel approachl
I
First, there is a theoretical framework of problem solving and knowledge acquisitiona the ISP-DL fftror-y (Impasse -Success Problem Solving - Driven Leaming). Its purposes are to: describe and explain the continuous stream of aclions and verbalizations of the leamer while working on programming tasks represent a guideline for design decisions ol the system
motivate and constrain models of leamer's knowledge states and acquisition processes.
a An
Intemal Model or ,ttate Model diagnoses the aclual domain
knowledge of the leamer (rules and schemas) at different states in the knowledge acquisition process. It is designed to be an integrated part of the ABSYNT PSM ("internal" to it) and to perform orlire knowledge
ChopEt
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AcquisitionofF6ctionol Pldnnit| aa.l Pro{aMing KnowlerlSe 235
diagnosis based on computer-assessable data provided by the leamer's
inlemctions with the system. The State Model is the basis lor user-adapted help.
a
An Extemal Model or Proceff Model \s designeÄ to simulate the knowledge acquisition processes, problem solving heuristics, and (in future) motivational processes of the leamer on a level of detail not available to the State Model. The Process Model is not pan ol the ABSYNT PSM ("external" to it) but suppons the design of the State Model. The Process Model is an olfrir? model designed ro bridge rhe gap between the ISP-DL Theory and the State Model by providing hypothetical /edrons for the knowledge state changes represented in the State Model. For example, the Process Model should hypothesize in which kinds of situations which kinds of weak heuristics are prcferred by the leamer.
Thus, ISP-DL Theory, the State Model, and the Process Model are designed to be mutually consistent but serve different purposes. Figure I summarizes their intenelationships: 'Ihe ISP-DL Theory collltrols the development of the Process Model the State Model. Data a\al lable from the leamer while ^nd working with the system are: stating and testing hvotheses abou.t created solution pmposals, progmmming actions and the time needed for them, and verbalizations. Such data are used for online construction and updating of the State Model, and/or for offline development and testing predictions of the Process Model. The State Model is in part based on an Epeft Model
representing planning knowiedge and implementation knowledge of the ABSYNT domain. Both the State Model and the Expert Model are designed to provide user-adapted help d erplanations.
^
First we will briefly describe the ISP-DL Theory since it provides the "roof" lor the design of the ABSYNI PSM, the State Model, and rhe Process Model. Then theABSYNT PSM is presented. In the next section we will describe the State Model and empirical analyses of some of its predictions. In addition, we show which empirical predictions follow lrom rhe State Model for differenr kinds ofhelp information ifthe adaptivity of rhe information to rhe leamer's knowledge is varied. Finally, the Process Model is described.
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C. Möbß ond O. Schrit
let
The ISP-DL Theory As indicated, the ISP-DL Theory is intended to describe the continuous stream of problem solving and leaming of a student as it occurs in a sequence of, lor
example, progmmming sessions. Empirical analyses of students' sessions working with ABSYNT (M öbus & Thole, 1990: Schröder, 1990) showed that such streams can be described as an interplay of Foblem solving, impasse-driven leaming, and success-driven leaming. Several approaches have been concemed with these processes, van tthn's theory of Impasse-Driven Leaming (van l,€hn, 1988, 1990, 1991b), SOAR (Laird, Newell & Rosenbloom, 1986, 1987; Newell, 1990; Rosenbloom et al., l99l ); or knowledge compilation mechanisms as, for example, incorporated in
AcI*
(Anderson, 1983, 1986, 1989) or described by wolff (1987, 1991). Consequendy, lhe ISP-DL Theory is an attempt to give an integrated account of the phenomena described by these and other approaches. The ISP-DL Th€ory has the following features (for more detarl see Mdbus, l99l b; Möbus, Schröder, & Thole, in press): a The distinction of differcnt problem solving phases (according to collwitzer, 19m, l99l).ln the Deliberute Pluse, the problem solver (PS) thinks about several goals. A goal is a set of facts which the PS wants to become tnre (Newell, 1982) and can be expressed as a predicative description. This phase ends vr'hen the PS chooses one goal to pursue: The PS is now committed to an intention. In the second phase, the PS pldrs a solution for the chosen goal. A plan is a partially ordered sequence or hierarchy of subgoals which may be created by domain-specific operators orbyweak heuristics.In the third phase, the plan is executed, and ßnally the result is evdü.,ated. For example, the
PS may check whether the obtained result satisfies the predicative description representing the main goal.
a me
impasse-driven
acquisitio of nert knowledge, Rott9hly,
aat
impasse is a situation where "the architecture cannot decide what to do next given the knowledge and the situation that are at its cufient focus of attention. " (van Lehn, l99lb, p. 19). Impasses may arise at different poiots in problem solving (Newell, 19m, p. 174). Forexample,lhe PS may not be able to d€cide on a goal, or to synthesize a plan, or a plan might not be executable, or there are no criteria to evaluate a result. [n response to impasses, the PS applies weak heuristics, like asking questions,looking for help, chealing, and soon (Laird, Rosenbloom, &
Atapter
I
I
Acttußition
d Ftnctional Plannins an ! PmNaMinß Kno\|ledß. 231
SP-DLTh.ory ABSYNT Problem Solving
Erremal
nal SlAre
Dara
Model
Model
Elpen Model
FiSuE
l:
The inlerelaliorships belwe€n ISP'DL Tbeory. the Process Model, üe StaE Model, the Eipen Mode, üe data o{ fte leamer, and help and explamtions.
Newell, 1987; van Lehn, 1988, 1989, 1990, l99lb). As a result, new knowledge may be acquired that leads to overcoming the impasse. So, impasses are situations where the leamer is likely to actively look for &elp (van Lehn, 1988). But ir is also possible that the information obrained is not helpful. For example, information intended as help may be loo complicated, orcodusing, or lead in awrong direction. So instead ofsolving the impasse, a secondary impasse may arise, as aheady described by Brown and van Lehn (1980).
a
me success-driven inprorement of acquired knolel€dge. Successfully used knowledge (knowledge which application did not lead to an impasse) may be improved so it may be used more effectively in the future. More specifically,by rule composition (Andeßon, 1983, 1986; Lewis, 1987; Neves & Anderson, 1981;Vere, 1977) lhe number of control d€cisions and subgoals to be set may be reduced, because fewer rule selections have to be performed. In contmst to these authors, our composition is based on resolution and unfolding (Hogger,l990), se€ Möbus, Schröder, and Thole (1991; in press). This has theoretical and empirical advantages.
C. Maibus and O.
Schtdd.r
The ABSYNT Problem Solving Monitor ABSYNT ("Abstract Syntax Trees") is a functional, visual programming language based on ideas stated in an introductory computer science textbook (Bauer & Coos, 1982). ABSYNT is tree representation ol pure LISP and is aimed at supporting the acquisition of basic functional programming skills, including abstraction and rccursive systems. The design of ABSYNT as a risual programming language was based on'
a
heo altcmatire aecutable specwations of the ABSYNT interp.eter (Möbus & Thole, 1989; Miibus & Schröder, 1990) which were developed according to cognitive science principles and constraints (Larkin & Simon, 1987; Pomemntz, 1985)
r
empirical studies (Colonius et al., 198?; Schröder, Fmnk & Colonius, 198?) cofterning the mental representation of and misconceptions about fu nctional programs.
This work served to prcpare the development of the ABSYNT PS M (Kohnert & Jante, 1988/91) according to principles of visual leaming environments (Glinert, 1990). The motivation and analysis of ABSYNT wilh respect to properties of visual languages is described in Miibus and Thole (1989).
al iconic ptogrcn ninq environment (Cha'rg, 1990). Its rnain cornponents arc a visual edirol, a visua\ trace, and a help componen|, a hypotheses testing environmeü,'fhe design of the ABSYNT PSM is motivated by the ISP-DL Theory in several respectsl
The ABSYNT PSM provides
a
According to the ISP-DL Theory, the leamer will look for and appreciate help if he or she is caught in an impasse.without an impasse there is no need for help. So the ABSYNT PSM does not intenupt the leamer (see, for example, also Winkels & Breuker, 1990), but oj?ls help. As a side effect, this design principle provides valuable data about the student's impasses.
t
According to the ISP-DL Theory, the leamer should be prevented from trapping into secondary impasses which may lead away from the original problem solving. This may be done by letting the leamer make use of his pre-knowledge at impasses as much as possible. ln the
ABSYNT PSM, this principle is realized by the hlpotheses testing T'I'P- leafiet may state hypotheses about which pan of his cunent solution proposal he considers correct. The system then approach.
analyzes the hypothesis and gives feedback. The student can also ask
chapte,
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Acqußitioh
oJ
Functional
Plann4
aad
ProsruMinE Kno\|kAse 239
the system forcompletion proposals (see below). Another reason for the hypotheses testing approach is that in programs it is usually not possible
to absolutely localize bugs. Often the bug consists of an inconsistency
between program parts, and there are several ways to
fix it.
The buggy prograrn to the PS. Again, a side effect of the hypotheses testing approach is that it provides a rich data source of the leamer's problem solving. hypotheses testing approach leaves the decision how to change
a
a
According to the ISP-DL Theory, help should be provided at different levels of problem solving. The ABSYNT PSM suppots the problem solving phases ol planning, executing, ar'd evaluatitg solütion proposals. A solution proposal may be planned first by using goal nodes. So the leamer may create a plan and test hypotheses about it without bothering about its implementation at this stage. The
implementatio of the goals (thus creating an executable program) may be done later Finally, erahmtion is again supported by hypothesis testing.
Figure 2 depicts snapshots from the ABSYNI PSM. Figure 2a shows the visüal editor vherc ABSYNT programs can be created. There is a head window and a body windo\r. On the left side of Figure 2a, there is the tool bar of the editor: The bucket is for deleting nodes and links. The hand is for moving, the pen for naming, and the line for connecting nodes. The "goal" node will be explained below. Next, there arc constant, parameter, and "higher" operator nodos (to be named by the leamer, using the pen tool). Constant and parameter nodes are the leaves of ABSYNT trees. Then several primitive operator nodes follow ("if', "+",'r", "*", ...). Editing is done by selecting nodes with the mouse and placing them in the windows, and by linking, moving, naming, or deleting them. Nodes and links can be created independentlyt If a link is created before the to-belinked nodes are edited, then shadows are automatically created at the lirik ends. They serve as place holders for nodes tobe edited later. Shadows may also be created by clicking into a free region oia window.
Constant, parameter and operator nodes arc implementat o, nodes, A syntactically correct ABSYNT program is executable il it consists only of implementation nodes. Implementation nodes have three horizontal parts: an input stripe, a name strip€, and an output stripe (Constantnodes have only two stripes because name and output are identical). In the üsual trace of the ABSYNT PSM (not depicted), inpur and output stripes are filled with
244
C. Miibus
ad
O. Schtiider
0
0
I
E
e t3
E
c E Figure 2a: Sudent's eroneous and ovedy complica@d proposal in the visünl editor.
Figüre 2b: Sudenfs hypolhesis (bold nodes and links). Figure 2: Snapshots ofprobtem solving with ABSYNT: Studenf s proposal 10 thc REVERSE prcblem (2a), sluden!'s hypotlesis proposal (2b). fcedback lrom üe ABSYM system (2c). a.d the compledon proposar of üc ABSYNT system (2d).
11 Acqu4ition ol Furctio4al PlaMinE @d Programins Knowledse 241
Chaptzt
Figle 2c:
o
PosiLive teedback from
1993 Ass@ndon
FtSur€
üe ABSYNTsystm tolhe srudenr's hyporhBis
of Advanccmenl of conputing id Educlrion (AACD
2d: Completion proposals of
the
ABSYNT system on student dcmand.
computation goals and obtained values, so each computational step ol the ABSYNT interpreter can be visualized (Möbus & Schröder, 1989, 1990; Möbus & Thole, 1989).
242
C. Möbus and O.
Schrtd.t
But as already indicated, in ABSYNT therc are also Sral nodes designed to sl!;Toft delibetuting and pldrniaS. Clicking on the "goal" symbol in the tool bar (Figure 2a, on the left) causes the tool bar to switch !o the actual goal nodes. Goal nodes reprcsent more abstract plan fragments which may be implemented in several ways by implementation nodes or subtrees. Visually, goal nodes have no intemal structure. In Figure 2a, "LIST EMPTY" and "CASE' are examples of goal nodes. Each goal node is precisely defined as a predicative description for the yet to be implemented program fragments. For example, 'LIST EMPTY' represents the goal to test whether a list is empty. The "CASE" node rcpresents the goal to Prograrn conditionalized expressions, that is, condition-expression paiß. The ABSYNT goal nodes are based on a task analysis whichapplies the tnnsfornatiol, approach developed in the Munich CIP Project (Bauer et a1., 198?; Partsch, 1990). The transfomation approach ensurcs that a solution can be derived to a Siven task that is conect with respec! to the task description. Cunently ABSYNT supports 42 programming tasks. For each task, there is a goal node with a predicative and and lists.
a
verbal task description. Data types are numbers, truth values,
In Figure 2a, a wrong solution proposal for an ABSYNT program reversing a list is just being created. There are nodes not yet linked or even completely
unspecified (shaded arcas). As Figurc 2a shows, goal nodes and implementation nodes can be mixed ("mixed terms") within a proposal. The solution proposal in Figure 2a means:
llL
ß equ.l lo
Lhe
valuc old yet unknown e\prersion.
then the value of REVERSE is NIL, else il L is m enply lis! if the value of a yet unkno*1l exp.ession is the empty lisl then üe valE of REVERSE is tte value of L, ele the value of REVERSE is obtained by CONSing üe välues of two ve1 unknown exprcssions bgether.
üen
parts ofthe program in Figpre 2b) about the conectness ofa solution pmposal
or parts thereof for a given programming task. The hypothesis is: "It is
possible to emb€d the boldly marked fragment of the program in a correct solution of the cufient task!". The system then analyzes the hypothesis. the hypothesis can be confirmed the PS is shown a copy of the hypothesis (Figure 2c).Ifthis information is not sufficient to resolve the impasse, the PS
If
may ask for more information (completion proposals, Figure 2d).
lf
the
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Acquisition ol FunctiMl Plannin| and PrcSraMiag Knon'lzdEe
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hypothesis cannot be confirmed the leamer receives the message that the hypothesis cannot be completed to a solution known by the system.
In Figure 2b the leamer stated a hypothesis which covers a fmgment of the proposal created so far for the "reverse" progmmming task. The hypothesis contains goal nodes and implementation nodes. The system recognizes the hypothesis as embeddable, indicating this by retuming a copy of the hypothesis to the student (Figure 2c). If this information is not sufficient for solving the impasse, the student may ask the system forcompletion proposals at the open links. In Figurc 2d, the student asked for and received six
completions (bold). Two
of
them are goal nodes, the others
are
implementation nodes. The "REVERSE" goal node represents the task goal. As far as possible, the system tries to generatecompletions consistentwith the student's proposal. At one point, the system disagrees with the student's proposal: The system proposes "LIST NOT EMPTY" at the third input link of the CASE node, whereas the student's original proposal contains "LIST EMPIY" at this point (Figure 2a). Intemally, the system has created a complete solution, but the student always gets only minimal information. The hypotheses testing environment is the most significant aspect where the ABSYNT PSM differs from other systems designedto support the acquisition
of functional prograrnming knowledge, like the LISP tutor (Anderson & Swarecki, 1986; Anderson, Conmd, & Corbett, 1989; Corbett & Anderson, 1992), the SCENT advisor(Greer, 1992;Greer, Mccalla, & Mark, 1989), and ELM system (Weber, 1988, 1989, 1992). As indicated, one reason for the hypotheses testing approach is that in programming a bug usually cannot be absolutely localized. Hypotheses testing leaves the decision which parts ofa buggy solution proposal to keep to the studeDt and thereby provides a rich data source about the leamer's knowledge and intentions. Single subject sessions with the ABSYNT PSM revealed that hypotheses testing was heavily üsed. It was almost the only means of debugging wrong solution proposals, despite the fact that the subje{ts had also the visual trace available. This is pardy due to the fact that in contrast to the trace, hypotheses lesting do€s not require a the
complete ABSYNT progmm solution. Hypotheses testing is possible with incomplete solutions, with goal nodes, and with mixed terms. So the student may obtain feedback whether he is on the right track at very early planning stages.
The answers to the leamer's hypotheses are generated by mles defining a goalsiteans-relation(GMR) (Levi & Sirovich,l976; Nilsson, 1980). A subset of these rules may be viewed as "pure" expert domain knowledge not
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C. Miibus a^d O. Sch/iidet
influenced by learning. Thus, we call this set of rules EXPERT. Currendy, EXPERT contains about 1300 planning rules and implementation rules. The planning rules elaborate goals and the implementatioo rules describe how to realize goals by ABSYNT implementation nodes.The goal decomposition
done by the planning rules follows the CIP transformation approach mentioned earlier. EXPERT is able to analyze and to synthesize several millions of plans and solutions for the 42 tasks (Möbus, 1990, 1991; Möus & Thole,1990). we think that such a large solution space is necessary because we observed that subjects, especially novices, often construct unusual solutions due to local repars.
The completions shown in Figure 2d (bold program fmgments) were generated by EXPERT rules. EXPERT analyzes and synthesizes solution proposals, but is not adaptive to the learner's knowledge. Usually EXPERT is able to generate a large set ofpo,r,tiöle completions. For example, EXPERT could genemte a large number of alternatives for the "LIST NoT EMPIY"
goal node in Figüre 2d: for example, lhe goal nodes NOT, EQUAL, GREATER THAN 0 (with respect to the length of the list), or the implementation nodes =, *. Thus, the problem is to relectthe most appropriate completion proposal. This is the main function of the intemal State Model, It represents the actual knowledge state of the leamer and consists of rules derived ftom EXPERT. The State Model should choose a completion which is maximally consistent witi the learner's current knowledge state. This should minimize the leamer's surprise to feedback and completion proposals. The State Model is implemented, but not yet integrated into the ABSYNT PsM. It will be described in the next section. To close this section, Figure 3 gives a summary of the components involved in planning, progmmming, and hypotheses testing in theABSYNT PSM. The leamer solves problems, acquires new knowledge due to impasse-driven learning, and optimizes knowledge due to success-driven learning. In Figure 3, the PS created a partial plan to the "even" task: "program thattests whether a natural number is even." The situation sho\ s a very early stage of program development. As can be seen from the screen the Ps is trying to do case analysis. His decision was to splitthe "even" problem into twocases. ThePS defined the first case as "N EQUALS 0". Under this condition the goal "EVEN" has still to be solved. There is no proposal for the second case. The PS knows only that under the condition of the second case the original "EVEN" problem has to be solved. when the PS states a hypothesis, the system analyzes it, that is, it diagnoses the intentions (planning steps) and the
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11
Acq\isitioa of rurctional
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actions (implementation steps) of the PS. The diagnosis ol actions and intentions leads to an updating of the State Model, and to positive feedback, enor messages, or help (completion proposals) which are tailored to the leamer. The learner will process this information (acquire new knowledge,
optimize knowledge) and continue with programming, planning, or hypotheses testing. Figure
3
also shows the place of the intemal process model
in this framework.
The Internal State Model The State Model is designed as an integrated parl olthe ABSYNT PSM.
It
represents the actual hypothetical domain knowledge of the leamer at different
points in the knowledge acquisition process. The hypothetical domain krowledge is organized as apartial orderofzicro rules, schemas,utdslf".ific cas6. Micro rules represent knowledge newly acquited by impasse-d ven
learning
bü not yet
optimized. They describe small planning or
implementation steps in the ABSYNT domain. Schemas and cases are created by rule composition according to the resolution method (Möbus, Schdder, Thole, in press). The State Model is created and updated by automatically inspecring the single editing steps perfomed by the user while constructing ABSYNT programs (Mitbus, Schrijder, & Thole, 199 l, in press). It is constructed according to the
following, simplified description: a After each programming task solved, the action trace of the PS is parsed by themicm rules, schemas, andcases of the State Model and (as lar as needed) by EXPERT rules. (For example, belore the leamer has solved the first task, the State Model is empty, so the first solution has to be parsed completely by EXPERT rules.) According to Corbett, Anderson, and Patteßon (1988) we call this process model tracing,
r I
The composites of all rules just used for parsing are crcated. Each rule used for parsing and each new compositejust created is checkedfot plaßibilit!. A rule is consideredplarrirte with respect to an action trace if the ABSYNT prograft fragments specified by
this rule are contained in the action tmce in an uninterrupted temporal sequence.
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Functi^al PIatuihS
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Pto|rcnning Knowtedse
A7
Each rule just found plausible is put inro the State Model if it is not yet contained in it. For each plausible rule already in the state model, its credit value is raised. For composites (schemas and cases), there
are two additional requirements: The part of the subject's action trace described by a composite must have been peiorlJj.ed earlier, and the actual sequence has to be performed/asrer than at that earlier
time. This is because composites are designed
to
represent
knowledge optimization.
4 illustrates some of the features of the State Model. lt depicts a continuous fragment of a sequence of programming actions performed by a subject. These data and associated times are stored in the action trace. To give an example, there is a micro nrle in EXPERT which describes the following four actions: Placing an ABSYNT if-then-else node, andcreating three input connections to it. In Figure 4, these four actions are performed at I I I 15:52, Figure
11:15:58, 1l:16:46, and l1:16:55 (fragments wilh bold margins). So the actions coresponding to the "if-then-else-node" rule is interrupted at I I : l6:42 and I l:16:50. So this flrle is not plausible. This exaftple illustrates that lhe State Modelis created online based on detailed datat individual programming actions. As indicated, the purpose ofthe State Model is to pmvide individualized help
and completion proposals.
It
also gives rise to empirical predictions
conceming verbalizations and order constraints on progmmming actions. For example, it says that as the leamer shifts from novice to expert (that is, acquires süccessively more schemas and cases), there will not only be less
verbalizations and more performance speedup, but also different order constraints for solution steps. Figure 5 illustrates this. The upper part of Figure 5 shows a set ol four micro rules, and a set of two schemas. Each rule or schemais abstractly represented as a goals-means-pair (a goal tree 9... and an ABSYNT program fragment a...). The State Model postulates that ifthe leamer applies a certain rule or schema, then the corresponding programming action(s) should be performed,
and vice versa. If the leamer verbalizes an intention, there should be a conesponding goal in the rule assumed to be applied. Conversely, for goals not part of the rule, there should be no verbalizations at all (middle part of Figure 5). Together \rith the concept ofplausibility built into the State Model, this means that if the learner applies a cenain nrle or schema, then the corresponding action sequence of actions and goal verbalizations should be pedormed in an uninterrupted sequence. Actions and verbalizations stemming
248
C. Miibus a^d O. SchtiiAer
l---ll=-lltH Ht
I ll
.lltH l. -l ./l
ll
cl
t4 tl F
.)
HHHH -rIUJ
)r-,4 =tt.
o FigurE
1992
As$cidion of Advlncenent of computine in Educ0lion (AACE)
4: A conlinDoDs fragmenr of a squence of programming acdons perfomed by a subject.
i
from different rules stauld not terleave (no-interleaving hypothesis). So if the State Model contarns the set {rl, 12, 13, 14} of micro rules, then an empirical sequence like [92, al, a2, ...] should /rot be obsewable (Figure 5) because al interrupts the sequence of events [92, a2] explained by 12. But an event sequence like [92, a2, cv, a4,94, ...1is consistent with the set { r1, O, 13, r4): there is no interleaving of events explained by different rules. "cv" denotes actions and verbalizations, like moving and rearanging nodes and lin16, which are indicators of control or heuristic processes. These control events could occur "between" events of different rules. They also should not interrupt an event sequence explained by one rule. Control events are to be explained by the extemal Process Model. For the two schemas {s1, s2}, the prediction is that the data explained by sl should not interleave with the data explained by s2. Again, control events could occur "between" schema events. As Figure 5 shows, the event chain [g2, al, a2,...] which was inconsistent with {r1, 12, 13, r4l is conrirt r with { sl, s2l, but an event chain like [al,93,92, ...] is not, because al and 92 stem from the same schema but are interrupted by g3 . So schemas lead lo weaker
Chapt /
Il
AcquisitionofF6ctional Planniq and PnsraMiaq Knodedqe 249
Set of micro rules:
I tl
@t,
13 (s3,
al), f2(82,^2), a3), ra G4 aa)
)
set of schemas:
{ 3l(
\.1 gt
'Y
L2
E4
s2(
'Y '4t
I
Action and verbalizadon predictions: Data: Model: acdon goal goal
verbalizadoß
---> -
-
ve.balirrtior
No-interleave prcdicdons for {rt, 12, 13, 14 }l aot: lt?, st, a2, ct, a4, 83,33, g1l tut lA2, a2, cr., a4, 84, c\,43, 83, cv, t l , 0l l or 1a3.83, cv,92, a2, cv. tl. gl. cv,84, .41 or ". No-interleave predictions for
[sl, s2):
daB(sl) b€forE dab(cv) befo€ dah(s2) or dara(s2) before data(cv) beforc d&ta(sl)
Nt: la\,
E3,92, a3, s4, sl, A',
but lez, aI,
a2, 91,
cv,,4,
83,
^4') Eal ot ß,
.
Time-interval preöctions time-ht€rval(lsl, s2l) < tim€'in@dal(lrl, 12' 13' 14l) . cv
FigDrc
is
a
abbreviation for: control a.tions
5: Empirical pßdiclions of
a
veöalizations
the Stale Model for micro
dles
vs-
shemas.
order constraints than micro ntles. BtJt therc are more predictions of the State Model: The application of the schemas should be faster than the application of the micro rules (bottom ofFigure 5) because less control decisions have to be made by the learner (time hypothesis). For the same reason, we would
expect less contlol actions and verbalizations, that is, Iess moving, rcpositioning, and rearanging ofnodes and linls (reaüanqement h)'pothesis),
of the predictions of the State Model have been tested empirically (Möbus, Schröder, & Thole, 1992). The ro-interleaving hypothesis was Some
250
C. Miibus a^d O. Schriidet
investigated in the following way: The action and vertalization sequence of a single subject working with rhe ABSYNT PSM was videotaped and categorized, and the State Model was run offline based on the solutions created by the subject. This led to a sequence of consecutive hypothetical knowledge states ofthe subject. Based on this state sequence, it was predicted which actions and verbalizations of the subject should occur in uninterrupted s€quences. This resulted in the model trace (Figure 6, on the right) which consists of sets. Each set of the model trace coresponds to the application of one State Model nrle. For example, at the state depicted in Figure 6 the State Model contains a rule that describes three programming actions: to place an ABSYNT "product" node, and to dmw two input lints for it. So the actions
and verbalizations of each model trace set are expected to occur in a continuous uninterupted sequence. The ,r,.rject trace (on the left of Figurc 6) is the actually observed action and verbalization sequence. The subject trace was compared to the model trace in the following way: For each adjacent pair of events of the subj€ct trace, if both events are contained in the same model trace set, then a
"+"
was assigned, otherwise a
'!"
was assigned.
For example, in Figure 6 action events 36 and 37 belong to different model trace sets, so a "-" is assigned. (On the left of the subject race, a slightly different but equivalent meüod of assigning "+" and "-" is shown.) So "+" denote correspondencies of model tmce and subject trace, and "-" denote contradictions. The whole subject tmce contained 76 "+"and 60 '!". Since more "+" should lead to longer and thus fewer runs (continuous sequences of "+" and':") than an equal distribution of "+" and "-", the Runs test was
applied. There were 42 runs (p < 0.001), which is consistent with the ncinterleaving hypothesis. In addition, many of the discrepancies ("-") between model trace and subject trace are due to the constant and parameter node rule (see for example events 36 and 40 in Figure 6).
How can the State Model contribute to user-adapted help generation within the ABSYNT PSM? Obviously, it should select the completion proposal to present to the leamer, so the leamer will receive Proposals which are maximally consistent with his pre-knowledge.
But the State Model is also capable ol identifying knowledge gaps knowledge not yet acquired by the PS but necessary !o continue with the actual solution proposal. Based on such a diagnosis, new em pirical predictions are possible because the completion proposals selected as help by the system can be vaded according to two dimensions: Srditr size and amounL If lhe size is ,tne, the completion proposal may rest on a chain of micro rules
9tuin
Chapkt 11 Acqußition ol Functiüal Ptuain8 and PtosaMinq Knowled* 251
Ev€nt no.
Model T!!c€
subje.t Trac.
{ {
ph..corBt nod€' w'ia. th.v.luc'!I"
lnto th. consbna nod.l plrc. product Dod€'
{r!.t
link rom lhe
producr
nd.
ao
tle
s€cond rnlnut node,
ctlat unt from th. lo lhe coNlint node
ao
lh. const.na nodc )
w;a. &e vrlue ".1"
iDoo th€ constant node
Figuß 6: Empidcal analysis of the StaE Model: Sübject lrace, model race, and the coftspondencies (+) and discrcpancies C) belween üem.
covering the gsp. For example, the completion proposal may consist of an ABSYNT subtree with an explanation of the goal sequence leading ro ir. If the grain size is cod6e, then the completion proposal may rest on a single composite. For example, the completion proposal may consist of an ABSYNT
subtree without any explanation. Concerning amount, the information provided may exactly I ll the Eap, ot too much information is provided, ot ?nougft information so that apart of the gap remains uncovercd. Different combinations of grain size and amount lead to different hypotheses. For exanple:
o
a
Ifthe information is fine-grained
a
If
and exactly fills the gap, then we would expect that the student considers this infofiation as helpful.
the information is coarse-grained and exactly
fills the gap then
the
student misses explanations. So s/he might eithetpassiyeb' accept what is being offered, or eng age in self-explanation (van Lehn, I 99 I a).
C. Möbus and O. Scb öaer
t
If the information is fine-grained but exceeds the knowledge gap' then the studoDt has to 'Flter" the content relevant to the current
I a
situation. This might be exlf.'ienced as burdensome. If the information leaves a small knowledge gap, then the student might try to indüce one new simple rule and thereby cover the rest of lhe gap. (This situation seems similar to the induction of one subprocedure at a timeby van Lehn's (1987) SIERRA program.)
Finally, the last case to be considered here is that there is a large gap left. and the infomation offered is too coarse. The student should experience such an information as very inadequate to his current problem. Thus she or he should feel annoyed or even upset.
There remarns much work, ofcourse, to work out these hypotheses and put them to empirical test. But we think we have shown that the State Model is an
empiricatly lruitful approach to knowledge diagnosis and adaptive help ge;eration which is testable and also touches upon fwther research problems, like motivation and emotion.
The Extemal Process Model The Process Model is aimed atmodeling the knowledge acquisition P,'ocess?s which hypothetically lead to the changing knowledge states as described by the State Model. It is conceptualized as a executable reatization of the ISP-DL architecture and tries to give an account of data not comPuter-assessable with
current technology, like the leamer's ve.balizations.
The precursor of the Process Model was a model of the acquisition ol a cosnirive skill in the domarn of lhe operational lnowledge (inlerPreler kr;wledge, about ABsYNT. based on a theoretical framework of knowledge acquisition (impd$e'a d success-driven leamirrg) which was the precursor of the ISP-DL Theory, and empirical analyses of verbal and action protocols. The starting point for this model consisted of two altemative visual rule sets based on executable specifications of the ABSYNT interpreter (Möbus & Thole, 1989). The visual fiile sets were used as help material for subjects while acquiring the operational knowledge (Möbus & Schrijder,l989' 1990). Rule specific hypotheses conceming memory representation and working memory load were disconfirmed (Schrijder et al.' 1990) Thereforc' a simulation model ofthe knowledge acquisition process was constructed and compared to adetailed protocol of verbalizations and actions (Schröder,1990,
Chaptet
1
1
AcE isition ol Functbnol Plannin| an l PtoEruD,lni,s Kiovledse 253
1992; Schriider
&
Kohnert, 1989/m). According
to the model, new
knowledge is acquired in response to impasses: lmpasses trigger problem solving processes which involve the use of the help material, and existing knowledge is optimized if used successfully. The model was compared in detail to a subject träce of actions and verbalizations. It was able to hypothesize, for example, which kinds of situations lead to which kinds of weak heuristics and corresponding actions. The extemal Process Model in the domain ofconstructing ABSYNT programs (see also Schröder & Möbus, 1992) was developed based on the ISP-DL
Theory and an empirical analysis
of a
subject trace (actions and
verbalizations) from a single subject session with ABSYNT. The analyzed pafi of the subject trace contained about four hours of problem solving. Figure 7 depicts the main components of the Process Model as a higher order Petrinet (Huber et al., 1990). Places (circles /ellipses) represent states (e.g., the content of data memories, mental objects like plans or impasses, or real objects like task descriptions or solutions). Irarsit ors (rectangles) represent events or pr@ess steps. The model consists ol the following steps:
a
The description ol
a
Based on the task representation, a pldn for a solution proposal is
a programming task is represented as a text graph. The first step is to ?..rde6tdrd the task by creating a propositional task representation (Kintsch & Greeno,l985; van Dijk & Kintsch, 1983) which is a hierarchy of concept names.
created by making use of domain knowledge. The domain knowledge is a set of concepts. Each concept has a name, an inpuFoutput desc.iption that can be calculated with example values, and (possibly) an implementation in ABSYNT. So a concept coüesponds toa micro nrle, a schema, or a case. But aconcept may be incomplete, the ABSYNT implementation may be missing. As asimple example, theconcept "multiplication of two numbers" may be known, butitsimplementation in ABSYNT maybe unknown. (So an incomplete concept represents the pre-knowledge before working with ABSYNT.) The plan consists of instantiations of concepts of the domain knowledge.
a
Afterthe plan is created, there are seveml possibilities. The simplest possibility is that the plan is executed. Alternatively, an impdss€ rnightarise. This happens ifthe plan cannot be executed because of missing ABSYNT implementation knowledge in one or more concept instantiations. Now several fter.rirticr are possible.
254
C. Mobus
ü.1 O- Schriidet
Figure 7: The extemäl Proces Model
ChapEt
1
t
Acqußinon ol Fu.ctiüal PlaMinB anr! Progrannins Knowledse 255
The first one is to look for help. The help material given to subjects
consisted of example calculations of the primitive ABSYNT operator nodes. So for each primitive ABSYNT operator, the concept in question is calculated with the same input values as the example calculations. Il the result is the same, then the primitive ABSYNT operator is inserted into the concept instantiation, and it is stored with the original uninstantiated concept as well (acquisition of new knowledge). Ifno such ABSYNT operator is found, then the heuristic has failed. Still the plan cannot be executed. The next heuristic (switch focus) is tried: Another part of the plan is implemented first. Ofcourse this does not solve the impasse, so the impasse will be encountered again. The third heuristic is restrucoring. An attempt is made to rcplace the concept instantiation by another one that has the same input-output behavior. (This is checked with example values). For example, the plan fragment to change the sign ofa numbercan be replaced by multiplication with -1. Il such a replacement is created, then it is stored in lhe knowledge base (acquisition of new knowledge), and the plan is changed accordingly. Otherwise the founh heurisric, analogy, is ftied. The analogical transfer is basically syntactical, but in addition, adjustrnents arc made in the target solution which are again based on calcularions wiü inpuFoutput descriptions.
I
After an executable plan
has been created and executed, the
resulting
ABSYNT program is eraluated by hypotheses testing.
If
the feedback is that the whole proposal is correct, then the concepts used with this task are composed, based on the executed plan, and the next task may be tried. If the feedback is that the proposal cannot be recognized by hypothesis testing, then the executed plan is debugged (= resolve impasse). Strategies of hypotheses testing and debugging are not yet paft of the model.
A trace of the model was stepwise compared to the subject trace of solving five programming tasks. One result was that 65qo (about 200) protocol categories of the subject trace were reprcduced by the model. What is the significance of the external Process Model fortheISP-DLTheory, theintemal State Model, and for help design?
a
Conceming the /SP-DL Theory, the Prcress Model specifies types of impasses, like missing implementation knowledge and negative feedback, and hypothetical weak heuristics and the conditions for
C Miibß ando Schrtder
256
their application. These hypotheses can be used to make the ISP-DL Theory more detailed and empirically testable.
Conceming the State Modet, the Process Model specifies when which new knowledge is acquired and optimized. So the Process Model gives hypotheses about how the knowledge contained in the State Model might be generated. The Prccess Model might also help to find out how to modify the State Model if its Prcdictions are disconfirmed. Conceming help design, hypotheses of the Process Model about weak heuristics can be used to design domain-r.rspecific, " strategic" should be possible to help. For example, with the model recämmend to the learner to look for analogies in ceftain situations, or to think about reformulating goals or to ask for their preconditions in other situations.
it
Conclusions We described an approach to dlagnose and model knowledge and knowledge acquisition processes, and to apply these results to user_adapted help Our approach has three levels:
a
theotetical fmmework, the ISP-DL Theory, of problem solving and knowledge modification a
a
an intemal State Model for online diagnosis and generation of user-adapted help
a
ar extemal Process Model for offline generation of hypotheses about impasses, weak heuristics, knowledge acquisition, and optimization'
The three levels me inlended to be mutually consistent but serve differcnt purposes. The ABSYNT PSM designed to support the acquisition of basiciunctional p.ogram*ing skills in a visual language is a concrete realization of this approach. In line with the ISP-DL Theory, it ofers help to the leamer to leamer's malce use of at impasses, it tries to be maximally consistent with the problem solving knowledge state by hypotheses testing, and it supports the is based states of-planning, ex;udon, and evaluation. Planning in ABSYNT ABSYNT executable leads to Execution on a transformation approach. programs, and evaluation is based on the hypotheses testing approach'
Chap@
11 Acqußito4 ol Functional PI@iinE
and ProEraMins KnowlzdEe 251
The intemal State Model represents knowledge states consisting of newly acquired and optimized knowledge, as rcquired by the ISP-DL Theory. It is continuously updated based on the online analysis ol small action steps. It allows a large amount ofprcdictions conceming the interleaving of action sübsequences, times, and Garmngements like moving and repositioning program fmgments. Some of these predictions were empirically analyzed. The extemal Process Model is designed to bridge the gap between the state Model and the ISP-DL Theory by providing hypothetical reasons (impasses, weak heuristics, ...) for the knowledge state changes described by the State Model. Further work will be directed to integrate the State Model and the Process Model into the ABSYNT PSM, to investigate the empirical predictions, and to Benerab explanations ol the system for positive and negative feedback in response to hypotheses testing, and to completion proposals now provided by the ABSYNT PSM.
Our three level approach has been developed in the context of functional programming, but is not constrained to it. In a related project, we develop a help system, PETRI-HELP, which is designed to support modeling concurrent or distributed prccesses with Petri nets (Miibus, Pitschke, & Schriider, 1992). A research goal is to study the question how much of the theory and models is domain independent.
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